Assignment:

Solve 2 questions.

1. Starting from the equation for the speedup factor given by
   
   $$S(n)=\frac{1}{f+\frac{1-f}{n}}$$
   
   
   show the inequality that relates the fraction of serial computation, f, and the number of processors employed, $n$, if a 50% efficiency is to be achieved.
2. Consider a parallel architecture built using processors each capable of sustaining 0.5 megaflop. Consider a supercomputer capable of sustaining 100 megaflops. What is the condition (in terms of $f$ ) under which the parallel architecture can exceed the performance of the supercomputer?
3. Consider an algorithm in which ($1/ \alpha$) th of the time is spent executing computations that must be done in a serial fashion. What is the maximum speedup achievable by a parallel form of the algorithm?